Stability and Bifurcation Analysis of Two-term Fractional Difference Equation

2025/09/23 by Janardhan Chevala, Sachin Bhalekar, Chevala, Janardhan +1
Mathematics · Physics and Astronomy · #39A30 39A28 #39A30 39A30 #Dynamical Systems (math.DS) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2509.18746

openalex publication_date 2025/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the linear equation including two fractional order difference operators, viz. Δ^α and Δ^β, 0<β<α≤ 1. The sequence representation will be provided to find the solution in an easier way. The Z-transform will be used to find the boundary of the stable region in the complex plane. If the coefficient of the operator Δ^β is negative (near 0), then we observe that the boundary curve has multiple points generating multiple stability regions. We provide all possible bifurcations in terms of parameters. An ample number of examples will be provided to support the results.

Citations

• Analysis of a Class of Two-delay Fractional Differential Equation
• Dynamical Analysis Of Fractional Order Generalized Logistic Map
• Fractional Order Sunflower Equation: Stability, Bifurcation and Chaos
• Stability and Bifurcation Analysis of Two-Term Fractional Differential Equation with Delay
• Stability Analysis of Fractional Difference Equations with Delay
• Fractional Order Periodic Maps: Stability Analysis and Application to the Periodic-2 Limit Cycles in the Nonlinear Systems
• Solving multi-term linear and non-linear diffusion–wave equations of fractional order by Adomian decomposition method
• p-adic discrete dynamical systems and their applications in physics and cognitive sciences

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